2000 Peugeot 206 intermittent starting problem

Hi my Peugeot 206 has developed an unusual intermittent starting problem, several garages have had a look at it and can't seem to diagnose the problem, so I would be grateful for any advice or suggestions.

When it starts there are no problems at all and it runs smoothly and never stalls. However sometimes when I try to start it, it is completely dead. There does not seem to be any pattern to it at all, the weather doesn't seem to effect it and nor does the time of day or the amount of time there has been since it was previously running. For example I drove it back from the garage on Tuesday and it was ok, didn't drive it yesterday but now it will not start at all however I if I try it this afternoon it might start or it might be several days before it will start again.
If anyone has had a similar problem I would be grateful to know how you resolved it as the garages I have taken it to run out of ideas. Thanks Shell